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Dimension of column- and rowspace

  1. Jan 19, 2008 #1
    [SOLVED] Dimension of column- and rowspace

    1. The problem statement, all variables and given/known data
    My book doesn't answer this question clearly, but I have notived the following connection:

    Does the dimension of the rowspace of a matrix equal the dimension of the columnspace of a matrix which equals the rank of the matrix?
     
  2. jcsd
  3. Jan 19, 2008 #2
    If the matrix has real elements, the row and column spaces have the same dimension. Furthermore, the rank of A equals the dimension of the row space of A.
     
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